A new propagation model coupling the offline and online social networks

  • Qian Shao
  • Chengyi XiaEmail author
  • Lin Wang
  • Huijia Li
Original paper


Although rapid advancements of online networking technologies and softwares (e.g., 5G, Internet of Things, Big data) have substantially facilitated our communications with others, the regular face-to-face contact is still an important communication channel in our daily life. Modeling the information diffusion through both online and offline interactions has become a challenging topic that has attracted much attention from the field of industrial informatics. To this end, we characterize the coupling effect of online and offline communication by developing a multilayer network propagation model, which considers three novel aspects: two distinct contagions taking place at two types of social software; competition and dynamic processes between them under the joint influence of individual selection and information dissemination; and information coupling between offline and online social networks. Moreover, a mean-field method is provided to analyze the critical threshold, and extensive Monte Carlo simulations are performed to demonstrate the theoretical predictions and explore the rich dynamical phenomena. Current results are conducive to understanding the transmission of information or epidemic spreading within the structured population, and further motivating the design of networked hardware and software with high performance.


Propagation model Multilayer network Offline and online networks Mean-field approximation Monte Carlo simulation 



We will acknowledge the funding support of the National Natural Science Foundation of China (NSFC) under Grant No. 61773286.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Tianjin Key Laboratory of Intelligence Computing and Novel Software TechnologyTianjin University of TechnologyTianjinChina
  2. 2.Key Laboratory of Computer Vision and System (Ministry of Education)Tianjin University of TechnologyTianjinChina
  3. 3.UMR2000, CNRSInstitut PasteurParisFrance
  4. 4.School of Management Science and EngineeringCentral University of Finance and EconomicsBeijingChina

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